Numeracy Practice. Dice

Numeracy practice tests

Firstly, this page focuses on Numeracy practice including our professional skills QTS numeracy skills test practice.

Secondly, here’s our Literacy practice tests page, which includes our professional skills QTS literacy skills test practice.

Professional Skills Numeracy Practice Tests

Practice numeracy test free download. This is our Professional Skills Test – Numerical Reasoning Practice Test for your practice.

Practice Professional Skills Test practice numeracy test answers free download.
These are our QTS Professional Skills Test – numerical reasoning online practice test answers.

Practice Professional Skills Test practice mental arithmetic test answers free download. These are our QTS Professional Skills Numeracy test answers.

Numeracy practise. Answering questions

QTS Numeracy test practice

Secondly, Practice QTS numeracy test free download. This is our QTS Numerical Reasoning Practice Test for your practice.

Thirdly, QTS numeracy test answers free download. These are our QTS numerical reasoning online practice test answers.

Fourthly, ractice mental artithmetric test free download. This is our QTS Mental Arithmetic Practice Test for your practice.

Finally, QTS mental arithmetric test answers free download. These are our QTS Mental Arithmetric practice test answers.

Practice Numeracy Practice Test 2 and Practice Numeracy Test 2 answers.

There are many different psychometric tests like the aptitude test, personality test, verbal reasoning, inductive reasoning, logical reasoning, attention to detail, leadership test and many more. Well, numerical reasoning assessment is one of them. This is where all the graphs, long numbers and equations play an important role. Since this is based on mathematics, the main objective of numerical reasoning assessment is to check the ability of the candidates to work with numerical information.

The numerical reasoning assessment is often a written test having a given time limit and its structure can be unconventional. The candidates taking this test often find it to be tricky or challenging when they compare it with their school or college level numerical tests.

Numerical test for employees

The employers who use these numerical reasoning assessments mainly evaluates how much snug you’re with numbers, basic mathematical functions and analyzing information underneath a substantial time pressure. It is no surprise, that corporation and organizations who take a look at their candidates with numerical reasoning tests typically place confidence in giant numbers and information.

Level of numerical reasoning

These tests are challenging for college students who have a mathematical background, therefore it is no surprise this could be a real problem for students who spent much of their time at the university reading or writing, instead of really tackling with huge numbers and solving various formulas.

Answering the numerical tests

Numerical Tests also come in the form of multiple choice questions. The answers, in contrast to with verbal reasoning tests, are going to be definite. That doesn’t mean it will be easier and this becomes the point of pressure and it is also the reason why the candidates find them so challenging.

Usually, candidates are provided with a variety of questions in accordance with the rule of one question = one minute.

Certain numerical tests have a repeated pattern and this gives you an idea on how to prepare for it. The common topics that you can prepare for include fractions, ratio and proportion, profit and loss, estimations, percentages, data analysis and graphical interpretation. So, ensure that you practice these portions thoroughly and make yourself comfortable with the different types of questions in these areas.

Numeracy practice test tips

There are always some tips that you can utilize while preparing for your numerical reasoning assessment which are as follows. These tips will easily help you to get through the numerical reasoning assessment easily.

  • Whether you would like to sharpen your number skills or learn everything from the beginning, taking some of the mock tests can help you to improve more. It would not turn you into an excellent mathematician in just one day; however, it will certainly improve your performance to a great extent. It will also prevent you from having too many sleepless nights before the assessment day by rising your accuracy, speed and confidence as well. And you may honestly want a good night’s sleep.
  • Don’t spend too much time on one question. Get a rough calculation of what proportion of time you have got per question before you begin every check and try maintaining those timings. If it feels that it is getting tough, keep going anyway, keeping in mind the fact that the best and easiest questions are yet to come.

More Numeracy Tips

  • While you are practising for the test, try doing it in the same way in which you’ll be sitting your real numerical reasoning assessment. Take your seat in a quiet surrounding with as less distraction as possible at a table. This will increase your focus and also make silence less intimidating and let you practice more thoroughly.
  • The numerical reasoning assessment will definitely not kill you but try to figure out the areas that you are getting wrong most of the time and practice those areas thoroughly. Focusing on those problems will help you to improve your overall test.
  • Thus, following these tips can be really helpful during the day of your numerical reasoning assessment. Do not stress. So, the type of job position you are applying for doesn’t matter, as it can be an investment bank, consultancy firm or the position of a manager, it is compulsory for you to take the numerical reasoning test.

Verbal reasoning test practice book

Firstly, Passing Verbal Reasoning Tests book by Rob Williams

Numerical Reasoning practice test book

Passing Numerical Reasoning Tests gif
Secondly, Passing Numerical Reasoning Tests book by Rob Williams

The Passing Numerical Reasoning Tests book contains Army practice numeracy tests. Also, Navy practice numeracy tests.

Numeracy Practice Tests Book Recommendations

Very clear layout to follow. Questions advance over the chapters. It sets a steady pace.

A very user-friendly and easy to read guide. Really focuses your mind on brushing up on your Maths skills. The author explains clearly how you can prepare to give your best for a test. Very useful and highly recommended.

Another really useful book by Rob. I will be recommending this to my delegates. It is clear, concise and, if you are applying for jobs with a strong numerical focus. The best £10 you will spend! I heartily recommend.

Great book and pretty hard numerical exercises.

Brilliant Passing Verbal Reasoning Tests.

5.0 out of 5 stars.

A MUST BUY for anyone attempting to pass any verbal reasoning test.

I highly recommend.

Very useful and good practice.

The book has a good range of tests. These reflect what comes up in real tests. So good practice for the real thing.

– – Numeracy practice tests – – –

Literacy Practice Tests Book Recommendations

An excellent guide to performing well in verbal reasoning tests.

It’s a helpful guide for anyone needing guidance. There are plenty of examples of the different levels of tests. I would definitely recommend this book to anyone taking verbal reasoning tests.

5.0 out of 5 stars. Highly recommended.

Just what I needed to further my career. Now I’ve tried the tests I feel more confident.

5.0 out of 5 stars. A must have for verbal reasoning test preparation.

This book is great. The explanations are excellent. Its helped me to see where I’ve been going wrong. The book has lots of examples which are relevant to the RAF aptitude test which I am studying for.

4.0 out of 5 stars. I definitely recommend to those who are preparing for these tests.

Found the layout of the book easy to follow. It has made the tests more accessible to me. It will hopefully help me in my job search.

Aptitude Test Design Projects

Rob Williams has over twenty years experience of bespoke psychometric test design, especially aptitude test designs. Plus ten years prior to this spent working for several of the UK’s leading test publishers. These include: IBM, OPP, SHL and HireVue.

Our consultancy work focuses on graduate assessment designs and aptitude test designs. 

Bespoke graduate assessment designs

Infact it is bespoke aptitude designs which are our speciality. Otherwise known as company-specific tests. With a bespoke psychometric test, organisations can design the content of their test(s) to match their own industry sector.

Understanding graduate assessments gives those applicants a competitive edge in today’s job market.

At a time when the graduate market is at its most competitive it pays for all graduates to perform their best on these psychometric tests. It makes sense to be prepared. Fortunately, there is a wide variety of practice material available, allowing graduates to familiarize themselves with the sort of tests they’ll encounter as part of the recruitment process.

Graduate assessment design

Graduate recruiters who want to minimise recruitment costs see online ability tests as an efficient and effective means of sifting the initial applicant pool. Verbal and numerical reasoning tests offer a reliable and standardised way to ensure that an optimal number of good candidates are seen by the business at the much more expensive ‘face-to-face’ stage. Chances are that this next stage will involve a retest in order to verify that the candidate who took the online test was who they said they were!

Online testing is particularly attractive for the ease with which multinational organisations can offer the same test(s) in a wide range of different languages to graduates around the world. The use of standardised tests in the recruitment process helps to ensure that applicants from different countries and from different ethnic groups are treated fairly.

We believe in the benefits of practice and ensuring fairness in testing. We therefore offer some practice aptitude tests and some practice psychometric tests. The intention is to promote as ‘level a playing-field’ as possible.

Bespoke aptitude test design

Our Personality test designs

Our situational judgement test designs

Aptitude test solutions

Our consultancy work focuses on aptitude test practice and bespoke psychometric test design. We believe in the benefits of practice and ensuring fairness in testing. We therefore offer some practice aptitude tests and some practice psychometric tests. The intention is to promote as ‘level a playing-field’ as possible.

Aptitude test design – Employability

All of our psychometric test practice resources are free. So, we hope you enjoy using them!   In our opinion, there is plenty of the right type of aptitude test practice, aptitude test tips and test-taking strategies.

We certainly hope you get maximum value from our free psychometric test practice resources!  Psychometric test practice works best when it’s specific to the test type and the level of difficulty of the psychometric test you will be taking.

Graduate Assessment designs for aptitude

Our first point is that a well-designed selection procedure focuses on predicting a graduate’s competency within a particular work context.

Secondly, that psychometric assessments only form one part of the selection procedure.

Our third point is that personality assessments can give an indication of how well an individual applicant will fit into the existing workplace or team.

Finally, psychometric assessments can assess which applicants are most suited to the demands of the vacant job in terms of both ability and personality factors.

Assessment Design / Psychometric Test Design

Aptitude test design example

Firstly, it’s fundamental to the use of any psychometric test is that users are aware of a test’s effectiveness and its known limitations.  This information is calculable through knowledge of a measure’s reliability and validity. 

Secondly, importance is attached to test results and decisions are made using test data.  Thirdly, you must be sure that the tests you are using have sound credentials and have been properly developed.

‘Bespoke’ Verbal Reasoning Test Design

Specific design criteria were applied.  Sufficient administration time was made available for a test taker to exhibit the appropriate reasoning ability. 

Other design criteria related to the target population groups. For example, this form of verbal reasoning test does not require the candidate to have any technical knowledge of grammar. Or to be able to spot minor errors in the spelling of unfamiliar words.

Practical examples are proved at the start of each test. Thus, test takers can familiarise themselves with the test format.


Many jobs involve working with verbal information and verbal comprehension forms a core component of almost all senior managerial roles.  The ‘Bespoke’ Verbal Reasoning Test measures the verbal reasoning skills that are fundamental to effective communication in such roles. 

In many organisations, verbal reasoning skills are key to the effective dissemination of business information across the workforce.

‘Bespoke’ Verbal Reasoning Test assesses how well an individual’s verbal reasoning skills can operate at a high-level.  In our opinion, primarily understanding written communication. Although, ‘Bespoke’ Verbal Reasoning Test also encompasses the ability to understand complex discussions.

Verbal reasoning is central to many roles. Thus the ‘Bespoke’ Verbal Reasoning Test is appropriate for a very wide range of senior job roles and tasks.


Many graduate and senior managerial roles require quickly extracting relevant information from written documents. And to make a judgement based on this information.  Thus ‘Bespoke’ Verbal Reasoning Test measures the ability to read. And to interpret a detailed block of text under strictly timed conditions.

The verbal information in the test appears in the form of passages of text. Each is followed by a series of 4 multiple-choice questions.  Each question requires relevant pieces of information to be extracted from the passage.And a specific judgement to be made on the basis of that information. 


After reading a passage the test taker has to read a series of statements referring back to information contained within the passage.  The test taker has to identify whether the statement is true. Or false. Or whether it is not possible to tell. Then to decide which is the appropriate multiple-choice answer to fill in. 

Each answer must be based solely on the information presented in the passage – ignoring any background knowledge that the test taker may possess.  The questions must also be answered without any interference from the test taker’s own beliefs about the subject matter. 

This reflects work conditions where there is a need to make objective decisions based solely on the information available at that moment in time.

Number of Items:          48

Test Time:         25 minutes

Time needed for Administration (including Test Time):     35 minutes


For each statement, fill in either T, F or CS on the answer sheet.

These corresponds to your decision as to whether the statement is True. False. Or whether it is not possible to tell.

T: True                    

F: False                   

CS: Cannot Say      

Three key psychometric pillars

These are often taken for granted – due to the fine efforts of HireVue’s and MindX’s R&D teams’ conscientious work!

  1. Standardization
  2. Reliability – means if I take the same test next week, my results will be similar.
  3. Validity – means the test measures what it says it measures. MindX knows which personality traits are measured because we have compared our results to well-established personality tests. HireVue validates its video assessments using high performer data and job analysis results.
  4. Being Non-discriminatory

 1. Standardization  

Since the first IQ tests were developed the whole point is to compare with a group of previous test-takers.

2. Reliability

There are two key types of psychometric reliability:

  • Test-Retest Reliability
  • Internal reliability.

Test-Retest Reliability

This concerns score consistency over time. If the test is measuring some stable characteristic of the individual such as intelligence, then the test should produce similar results if a group of candidates are examined using the same test at two points in time. The time gap between the measurement is important, as some psychological characteristics change considerably over time. Yet, a short gap of two weeks should not cause major changes.

Still, an external event in the period between the two assessment might cause a change, but here it is expected that the change will affect similarly all the candidates. This type of reliability is also known as test re-test reliability. It is assessed by correlating the tests scores measured first time with the test scores measured the second time. Ability tests are expected to have a reliability of at least r = .75, yet personality tests might have somewhat lower reliability.

Internal Consistency

The internal consistency refers to the question whether all the test items measure the same concept. It can be assessed in two ways. The first method is known as the split-half reliability which require correlating the score based on half of the test items with the score based on the other half (e.g., scores on odd and even items). Alternative method is item-total reliability which requires correlating each item score with the total score of the rest of the items. There is a statistical measure called Cronbach alpha that summarises all the correlations into one figure. A test should have an alpha of at least a = .80.

Aptitude test’s psychometric terms


Every psychometric test has at least one norm group.

The standalone score has little meaning, so a comparison with previous candidate performance is used. For example, percentile rank.

Pre-test (or Pilot) Item

A trial item as part of a larger-than-necessary set of pre-test items. The  final, refined test is created by refining those items that work best. This is based on statistical analysis of the trial item set’s results.

Aptitude Test Reliability

Firstly, is the test a reliable measure?

Most commonly the internal consistency index coefficient alpha or its dichotomous formulation, KR-20. Under most conditions, these range from 0.0 to 1.0, with 1.0 being perfectly reliable measurement. A reliable test may still not be a valid test.

Aptitude Test Validity 

Secondly, is the test valid? A measure of what it ‘says on the tin’?

In our opinion, both the initial content validation and later criterion validation analysis are vital for any bespoke psychometric test.

We recommend collecting additional recruitment data over time so that additional validation studies can be conducted. Such as assessment centre data.

There are many other types of psychometric test validation evidence, and one-off studies investigating a psychometric test’s criterion validity are common.

British Airways Aptitude Test Design Example

Blended assessment project:

  • Situational judgment test design;
  • Numerical reasoning test design;
  • Verbal reasoning test design
  • Personality questionnaire design.

For these two British Airways roles:

– Cabin crew assessment; and

– Customer service representative assessment.

British Army Aptitude Test Design Example

Psychometric lead role with Kenexa IBM; managing twenty associates.

  • We developed over twenty psychometric tests;
  • Situational judgement tests for Officers and for Soldiers;
  • Realistic job previews for Officers and for soldiers;
  • Ability tests (including problem-solving test) for Officers;
  • Ability tests (including a spatial reasoning test) for soldiers;
  • Officer personality questionnaire;
  • Soldier career guidance tools.

Aptitude Tests’ Vital Role

Many companies today are turning to testing and assessment tools to help them address these challenges and make more substantive and data-driven hiring decisions. Assessments are a great way to level the playing field and evaluate many candidates for the same skill sets in an objective fashion, using real-life technical scenarios that mirror the work they will be performing on the job. Automated assessment tools in particular can scale to make better use of your time and resources. Several key recruitment benefits are listed below.

Differentiation Benefits

Providing unbiased assessments is a great way to distinguish yourself to candidates in a crowded hiring environment. Candidates will see that you really care about hiring the most qualified tech workers in a manner that is unbiased and uncovers their true value.

Recruitment Cost and Recruitment Funnel Benefits

Automated testing helps you scale your recruiting efforts, evaluating many candidates simultaneously to save engineering hours, and ultimately the cost of those used hours, time and costs, which is particularly important for larger tech organizations.

Hiring, training and replacing a bad hire can cost almost 5x their annual salary. Making the right choice the first time around is vital to growing your business and keeping costs low.

Removing bias

Assessment tools give you a structured mechanism to remove bias from the evaluation and interview process. It’s completely objective, surfacing skill sets needed to succeed on the job without basing a decision on your intuition or gut feel. And it mitigates the disadvantage a candidate whose first language is not English may have in a traditional format.

Focusing on skills, not experience

Experience listed in a profile isn’t necessarily the most important indicator of true skills and expertise.

Assessments help you find candidates that may not have a lot of experience in a certain field. Bbut nonetheless have the skills you’re looking for.

Consistent process benefits

Assessment tools help you standardize your ongoing evaluation process. You’ll get an objective look at how candidates perform in the testing phase and can then compare it to their success on the job. A post-mortem can reveal how a good (or bad) hire performed in the assessment and help you to duplicate (or avoid) that performance in the future.

Our Practice assessment books 

Passing Verbal Reasoning Tests.


Numerical reasoning Tests.

Passing Numerical Reasoning Tests gif

Passing Numerical Reasoning Tests book reviews

Buy this book to pass!

Brilliant book. Read it from cover to cover. Don’t skip the chapters. I know it can seem patronising, the way he breaks it down, but I’d recommend reading it through.

Brilliantly practical and informative

What a great practical book. It starts from what is a numerical reasoning test, covers why numerical reasoning tests are used, who/how we use numerical reasoning, tips for test day and even helps you brush up on your Maths skills – yes all those little shortcuts you wish you remembered. More than 3/4 of the book is dedicated to actual practice test and not only the answers are provided, but also an easy to follow explanation of each. Definitely a worthwhile buy.

Very clear layout to follow, questions advance over the …

Very clear layout to follow, questions advance over the chapters and it sets a steady pace. This book helped me immensely to get all the practice I needed within 3 days.

A really useful book 

Numerical Reasoning reviews

Another really useful book by Rob. I will be recommending this to my delegates on interviewing/assessment techniques training; clear, concise and, if you are applying for jobs with a strong numerical focus, the best £10 you will spend! I heartily recommend.

Five Stars

Great book and pretty hard numerical exercises.

Useful, informative and good value

A very user-friendly and easy to read guide. Really focuses your mind on brushing up on your Maths skills. The author explains clearly how you can prepare to give your best for a test. Very useful and highly recommended.

Five Stars

Great book, tons of info and test to help you understand.

Great to get some practical help on how to succeed … at this stage of selection. I will recommend to anyone who needs to get through a numerical reasoning test.

Passing Verbal Reasoning Tests book reviews

Brilliantly practical advice

The advice and practical examples will answer all your questions about an impending assessment. The book is easy to read and covers preparation, practical examples and an overview of the usual proceedings on test day.

The author also highlights questions to be asked before test day and (I was very pleased to see) encourages feedback after assessment. The recaps at the end of every chapter are great for a quick overview before test day. Definitely a worthwhile investment and sure to put you at ease before an assessment of this kind.

A MUST BUY for anyone attempting to pass any verbal reasoning test.

Verbal Reasoning reviews

An informative yet easy to read book which helped me get through graduate level tests to the next stages of application. Would highly recommend.

Excellent sample tests and explanations

Passed the VRT for HMRC Legal Trainee Scheme this year after reading this book. Helpful.

Very useful and good practice

The book has a good range of tests that reflect what comes up in real tests – so pretty good practice for the real thing

Highly recommended

Just what I needed to further my career. Now I’ve tried the tests I feel more confident.

Good quality and light reading!

An excellent guide to performing well in verbal reasoning tests.

This book is an extremely well written and helpful guide for anyone needing guidance in how to perform well in verbal reasoning tests. There are plenty of examples of the different levels of tests. Clear explanations of the correct responses are given. I would definitely recommend this book to anyone who is facing taking verbal reasoning tests in pursuit of a new job or promotion.

Rob Williams Assessment – psychometric design specialists

Rob Williams Assessment Ltd have considerable experience in assessing test reliability test validity. This is a one of the key final stages in any psychometric test design. Most recently we have been asked to validate situational judgement tests. In addition to test the SJT reliability and to advise on suitable cut-off scores which minimise any adverse impact (due to gender, age, ethnic group and disability).

Many of the UK’s and US’s leading test publishers have used Rob Williams Assessment’s to assist with ensuring the psychometric properties of their trial psychometric tests. We consult on how to improve any test’s psychometric properties, particularly the test’s internal reliability and construct validity.

Our Assessment Toolkit

Strengths Assessment ~ Disability Assessment ~ Leadership Assessment ~ Situational Strengths ~  Intelligence Strengths Test ~ Skills test design / Psychometric ~ Assessment standards ~ Competency Design ~ Realistic Job Preview Design.

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